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Drupady [299]
3 years ago
10

How do you factor a²+2a+2 using imaginary numbers?

Mathematics
1 answer:
katovenus [111]3 years ago
5 0

Answer:

26

Step-by-step explanation:

a²+2a+2

4^{2} +2(4)+2

16+8+2

24+2

26

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3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k
Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt

Evaluate the integral to solve for y :

\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt

\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x

\displaystyle y = x^3+2x^2+kx - 2

Use the other known value, f(2) = 18, to solve for k :

18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}

Then the curve C has equation

\boxed{y = x^3 + 2x^2 + 2x - 2}

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2

The slope of the given tangent line y=x-2 is 1. Solve for a :

3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1

So, the point of contact between the tangent line and C is (-1, -3).

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2 years ago
Hector gather data from eight students who have accounts with to social networking apps about the number of people they connect
Natasha_Volkova [10]
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8 0
2 years ago
Show how to work the division problem 47 divided by 8 please
Dvinal [7]

Answer:

Step-by-step explanation:

47 divided by 8

= 5.875

hope this helps

6 0
2 years ago
Y=x^(2) -2x - 3 and y = x - 3
Oliga [24]

Answer:

(0, -3) and (3, 0)

Explanation:

1st equation: y = x² -2x - 3

2nd equation : y = x - 3

Using substitution method:

x² -2x - 3 = x - 3            <em>exchange sides</em>

x² - 2x - x - 3 + 3 = 0    <em>simplify</em>

x² - 3x = 0   <em>                 take common factor</em>

x(x - 3) = 0                    <em>simplify</em>

x = 0, 3

Solve for y:

when x is 0, y = x - 3 = 0 - 3 = -3

when x is 3, y = x - 3 = 3 - 3 = 0

5 0
2 years ago
Sum of series 1 +1/3 +1/3².... is?​
Charra [1.4K]

Answer:

The sum of the series is 3/2

Step-by-step explanation:

Given

1 + 1/3 + 1/3^2 + ....

Required

The sum of the series

This implies that we calculate the sum to infinity.

We have:

a = 1 -- The first term

First, calculate the common ratio (r)

r = \frac{1}{3^2} / \frac{1}{3}

Change to product

r = \frac{1}{3^2} * \frac{3}{1}

Solve

r = \frac{1}{3}

The sum of the series is then calculated as:

S_{\infty} = \frac{a}{1 - r}

S_{\infty} = \frac{1}{1 - 1/3}

Solve the denominator

S_{\infty} = \frac{1}{2/3}

Express as product

S_{\infty} = 1 * \frac{3}{2}

S_{\infty} = \frac{3}{2}

7 0
3 years ago
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